I've done the Iron Horse on a cross bike with 700x28 tires. At some points with deeper gravel, it was a struggle to stay upright. It was a very harsh and uncomfortable ride. Also, there are places where it's very pretty, but on the whole this isn't the most scenic route available. Plus, like other people mentioned, there's a tunnel to go through, so long (a few miles) that there will be no light except what you bring. It's moist and gravely in there. But there will be lots of creeks to drink from if you bring a purifier.
Sections of US 2 will be uncomfortable as far as traffic goes. But I think it's the better choice.
You can avoid the last 15 miles of Route 2 (the scenic Tumwater Canyon) if you go left at Cole's Corner, make a short detour at Lake Wenatchee, and then follow the Chumstick Highway into Leavenworth. This might add 5 or 10 miles to your journey, but it will cut the number of cars by 1/10th and every driver will be very polite and slow; if you stick to the highway they'll be fast and furious, sometimes passing you pretty close at 60 mph. Also, it's getting late in the year for the best scenery here.
If you get a good map, you can make it most of the way from Leavenworth to Wenatchee on back roads.